Bibi, a mother of five from Nankana area of Punjab province, was convicted of blasphemy in 2009 and has been on death row since 2010.
Her death sentence was upheld by the Lahore High Court in 2014 following which she lodged an appeal in the apex court.
A three-member bench of Supreme Court was set to start the hearing but Justice Iqbal Hamid-ur-Rehman, one of the judges, recused on the grounds that he also heard the case of slain Punjab liberal governor Salman Taseer.
He said that he already asked the chief justice to appoint another judge to the bench. It is unclear when the hearing will resume.
Taseer was killed in 2011 by one of his police guards, Mumtaz Qadri, when he termed the regulations "black law" following his meeting with Asia Bibi after her conviction.
Qadri was convicted for murder and hanged in February this year after his appeal was rejected by the Supreme Court. Justice Iqbal Hamid-ur-Rehman was part of the bench.
Blasphemy is a hugely sensitive issue in Muslim-majority Pakistan, which introduced the draconian laws in 1985 in a bid to appease right wing parties. These laws have been often alleged to have been misused to settle personal scores.
Militants also target people blamed for blasphemy or those demanding changes to them.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)